### Abstract

In the internal cytoplasm of interphase cells the density of microtubules is the highest in the centrosome area and decreases to the cell periphery. As a rule, the quantity of fluorescent microtubules cannot be counted up in the internal cytoplasm, but it is possible to estimate microtubules quantity using measuring of their optical density. In living 3T3 and CHO cells the microtubules optical density decreased according to different mathematical dependences that apparently reflected the differences of their microtubule system organization. To determine appropriateness that circumscribe the reduction of microtubules optical density from the centrosome region to the direction of cell margin, we modeled cell contours with the certain ratio and interposition of centrosome-attached and free microtubules in vector schedules CorelDraw program. The decrease of optical density was analyzed in MetaMorph program as it was described earlier (Smurova et al., 2002). It was shown that fluorescent microtubules optical density decreased exponentially (y = ae^{-bx}) if the system joined only microtubules growing from the centrosome up to the cell margin. The curve became smoother in the case of not all radial centrosome-attached microtubules reached the margin, and adding of free microtubules into the system led to the sharp fall in optical density in the centrosome area and to its gradual decrease at the cell periphery. The increase in free microtubules quantity changed the character of the curve describing the reduction of optical density microtubule system which included free and centrosome-attached microtubules in proportions of 5 : 1 was described by the equation of linear regression (f= k·x + b). Thus, the mathematical dependence describing the microtubules distribution from the centrosome to the cell periphery, depends on the ratio of microtubules and their relative positioning in the cell volume. The data obtained using model systems have coincided with the results of experiments. The graphs which described the increase in microtubules optical density during microtubule repolymerization after nocodazole treatment, corresponded to the graphs for model cells. Thus, the method we used allows to analyze the microtubule system in the cases when the direct observation of individual microtubules is difficult.

Original language | English |
---|---|

Pages (from-to) | 270-279 |

Number of pages | 10 |

Journal | Tsitologiya |

Volume | 49 |

Issue number | 4 |

Publication status | Published - 2007 |

Externally published | Yes |

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### Keywords

- Centrosome
- Centrosome-attached microtubules
- Free microtubules
- Video microscopy

### ASJC Scopus subject areas

- Histology

### Cite this

*Tsitologiya*,

*49*(4), 270-279.

**Free and centrosome-attached microtubules - Quantitative analysis and the modeling of two-component system.** / Smurova, K. M.; Alieva, I. B.; Vorobjev, I. A.

Research output: Contribution to journal › Article

*Tsitologiya*, vol. 49, no. 4, pp. 270-279.

}

TY - JOUR

T1 - Free and centrosome-attached microtubules - Quantitative analysis and the modeling of two-component system

AU - Smurova, K. M.

AU - Alieva, I. B.

AU - Vorobjev, I. A.

PY - 2007

Y1 - 2007

N2 - In the internal cytoplasm of interphase cells the density of microtubules is the highest in the centrosome area and decreases to the cell periphery. As a rule, the quantity of fluorescent microtubules cannot be counted up in the internal cytoplasm, but it is possible to estimate microtubules quantity using measuring of their optical density. In living 3T3 and CHO cells the microtubules optical density decreased according to different mathematical dependences that apparently reflected the differences of their microtubule system organization. To determine appropriateness that circumscribe the reduction of microtubules optical density from the centrosome region to the direction of cell margin, we modeled cell contours with the certain ratio and interposition of centrosome-attached and free microtubules in vector schedules CorelDraw program. The decrease of optical density was analyzed in MetaMorph program as it was described earlier (Smurova et al., 2002). It was shown that fluorescent microtubules optical density decreased exponentially (y = ae-bx) if the system joined only microtubules growing from the centrosome up to the cell margin. The curve became smoother in the case of not all radial centrosome-attached microtubules reached the margin, and adding of free microtubules into the system led to the sharp fall in optical density in the centrosome area and to its gradual decrease at the cell periphery. The increase in free microtubules quantity changed the character of the curve describing the reduction of optical density microtubule system which included free and centrosome-attached microtubules in proportions of 5 : 1 was described by the equation of linear regression (f= k·x + b). Thus, the mathematical dependence describing the microtubules distribution from the centrosome to the cell periphery, depends on the ratio of microtubules and their relative positioning in the cell volume. The data obtained using model systems have coincided with the results of experiments. The graphs which described the increase in microtubules optical density during microtubule repolymerization after nocodazole treatment, corresponded to the graphs for model cells. Thus, the method we used allows to analyze the microtubule system in the cases when the direct observation of individual microtubules is difficult.

AB - In the internal cytoplasm of interphase cells the density of microtubules is the highest in the centrosome area and decreases to the cell periphery. As a rule, the quantity of fluorescent microtubules cannot be counted up in the internal cytoplasm, but it is possible to estimate microtubules quantity using measuring of their optical density. In living 3T3 and CHO cells the microtubules optical density decreased according to different mathematical dependences that apparently reflected the differences of their microtubule system organization. To determine appropriateness that circumscribe the reduction of microtubules optical density from the centrosome region to the direction of cell margin, we modeled cell contours with the certain ratio and interposition of centrosome-attached and free microtubules in vector schedules CorelDraw program. The decrease of optical density was analyzed in MetaMorph program as it was described earlier (Smurova et al., 2002). It was shown that fluorescent microtubules optical density decreased exponentially (y = ae-bx) if the system joined only microtubules growing from the centrosome up to the cell margin. The curve became smoother in the case of not all radial centrosome-attached microtubules reached the margin, and adding of free microtubules into the system led to the sharp fall in optical density in the centrosome area and to its gradual decrease at the cell periphery. The increase in free microtubules quantity changed the character of the curve describing the reduction of optical density microtubule system which included free and centrosome-attached microtubules in proportions of 5 : 1 was described by the equation of linear regression (f= k·x + b). Thus, the mathematical dependence describing the microtubules distribution from the centrosome to the cell periphery, depends on the ratio of microtubules and their relative positioning in the cell volume. The data obtained using model systems have coincided with the results of experiments. The graphs which described the increase in microtubules optical density during microtubule repolymerization after nocodazole treatment, corresponded to the graphs for model cells. Thus, the method we used allows to analyze the microtubule system in the cases when the direct observation of individual microtubules is difficult.

KW - Centrosome

KW - Centrosome-attached microtubules

KW - Free microtubules

KW - Video microscopy

UR - http://www.scopus.com/inward/record.url?scp=34347325016&partnerID=8YFLogxK

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M3 - Article

VL - 49

SP - 270

EP - 279

JO - Tsitologiya

JF - Tsitologiya

SN - 0041-3771

IS - 4

ER -